[tex]A=\dfrac{1}{2}\cdot b\cdot h\\\\\\276=\dfrac{1}{2}\cdot(3x+10)\cdot x\qquad|\cdot2\\\\\\552=(3x+10)\cdot x\\\\552=3x^2+10x\\\\3x^2+10x-552=0\\\\\\a=3\qquad b=10\qquad c=-552\\\\\Delta=b^2-4ac=10^2-4\cdot3\cdot(-552)=100+6624=6724\\\\\sqrt{\Delta}=\sqrt{6724}=82\\\\\\
x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-10-82}{6}=-\dfrac{92}{6}\ \textless \ 0\\\\\\
x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-10+82}{6}=\dfrac{72}{6}=\boxed{12} [/tex]
So the height h = x = 12
